In addition to being good exercise, cycling is a good way to get around. Cyclists tend to make contact with locals much more easily than do other travellers. And of course you see a lot more of the countryside. The best time to try it is during the dry season, when pedalling will be easier and drivers stand a better chance of staying in control of their vehicles.
Football (soccer) is extremely popular in Gabon, as it is throughout the region. Pickup games in villages, universities and municipal stadiums are generally easy to get in. Basketball is also popular, and foreigners are usually welcomed into games.
Squash is popular in the capital and in Port-Gentil. You'll find tennis courts and swimming pools in Libreville and other large towns. Beaches at the larger hotels in the capital and at Port-Gentil offer decent sands, and some of them will rent you a sailboard. There's also some decent diving to be had near the capital.
There's some good hiking in Gabon. You can climb to the top of Mont Nkoum, near Oyem, or around the Boundji Waterfalls outside of Lastoursville. You can also go caving near Limbenga.